Garrett relation

The Garrett Relation postulates that there exists a fixed relationship between the world inflation-adjusted Gross Domestic Product, accumulated over all of history, and the current rate of global energy consumption. It was first identified in 2009 in a study of the forces controlling the evolution of world carbon dioxide emissions.
Observational evidence
The Garrett Relation applies to global quantities, not to individual countries or economic sectors due to the imbalances created by trade.
<math>C = \sum_i GDP_i</math>
The current rate of global primary energy consumption <math>E </math> can be related to cumulative production <math>C </math> through a coefficient <math>\lambda</math>:
<math>E = \lambda C = \lambda\sum_i GDP_i</math>
The hypothesized scaling defining the Garrett Relation is that the value of <math>\lambda </math> is a constant that is independent of the year that is considered.
Economic statistics from the Maddison database,
In traditional economic treatments capital is believed to be a physical quantity that possesses value independent of energy constraints. The Garrett Relation implies that an individual capital element has no value without an associated consumption of primary energy to actively connect it to other civilization elements. From this perspective, a very generalized metric of wealth lies in active networks of people and infrastructure rather than specific physical capital elements. Civilization has no value without energy consumption. In this way, if global energy consumption were to cease entirely, the value of civilization would rapidly tend towards zero. Not only current GDP would go to zero, but so would the inflation adjusted value of all past production go to zero. This is perhaps the most direct available way to see the connection of power consumption to not just current real GDP, but all past GDP summed as well.
A corollary of the Garrett Relation is that the global GDP is linked to the amount of physical work done to grow civilization's networks. For a net positive GDP, work must be sufficient to overcome natural network decay. The magnitude of decay in reducing real GDP is implicit in the Garrett Relation through the inflationary adjustment from nominal to real GDP, accounted for by the GDP deflator. a wider more explicitly thermodynamic interpretation of the classic , and also known as the Khazoom-Brookes Postulate. William Stanley Jevons observed that improving the energy efficiency of coal driven steam engines would lead to increased coal consumption as it would facilitate a stronger economy and enable mining coal at a faster rate. The Generalized Jevons' Paradox says that any improved civilization efficiencies will result in savings - savings which can and will be used to enable economic output elsewhere in the economy - and the additional output encumbers new energy consumption to support the new growth enabled
Energy efficiency, population, and some other traditional measures included as independent variables in standard economic models are, in this new view, seen to be dependent variables.
Decreasing the energy intensity of the economy has been suggested as a strategy for dealing with both limits to growth and rising CO<sub>2</sub> emissions. The Garrett Relation shows this is problematic. It follows from the Garrett Relation (Nolthenius (2018, p 262-264) that
<math>1/\lambda = \partial f/\partial t + (f/Y) \partial Y/\partial t </math>
where <math>f = E/Y </math>is the energy intensity of GDP, plotted on Figure 1 with historical data. Historically, <math>\lambda</math> , <math>f</math>, and <math>Y</math> are all positive. Thus, a prolonged global degrowth or recession with <math>\partial Y/\partial t<0 </math> implies increasing energy intensity.
Criticisms
Application of thermodynamics to human systems
It has been argued that complex human systems are not deterministic physical systems. Human systems exhibit highly complex behavioral changes in response to market forces that in turn alter markets. Such non-linear behaviors are not generally present in physical systems.
However, non-linear systems are observed throughout the physical universe and are not precluded by the Garrett Relation. Even if people exhibit learning and emergent behavior within evolving legal strictures and can be argued to exhibit free will, humanity is also subject to thermodynamic laws that constrain aggregate behaviors on global scales.
Relationship of energy to GDP
The relationship of global energy consumption to GDP has changed over time as the energy intensity of the economy has steadily declined (i.e. energy efficiency has steadily improved).
Accuracy of economic statistics
Inflation Measures: Decay in past economic production is implicitly accounted for by the adjustment from nominal to real GDP in historical statistics. Politically motivated biases may cause officially reported consumer price inflation (CPI), a major component of the GDP Price Deflator) to be lower than actual. For many policy and economic purposes, a desired inflation measure should correct nominal prices for changes in price levels of the changing goods and services in the economy. For example, trends in the U.S. economy show static or declining wages for most Americans, forcing substitution in consumption downward in the quality scale. Improper substitution procedures, it is argued, artificially bias CPI to be low. Correcting for this bias may make the historical Garrett Relation more constant than official data would suggest. to be as large as 26% of official GDP in the 1960s, but quickly declining to about 22% during recent decades. Incorporating the shadow economy into the Garrett Relation, however, actually makes the resulting trend over time of the ratio of integrated <math>C</math> to current power consumption more nearly constant, and thus supports more strongly the thermodynamic connections and validity of the Garrett Relation) uses the prices of a sample of nearly identical products between countries to convert between currencies, while "market exchange rates" (MER) uses real world market-driven currency exchange rates averaged over the relevant year. The Garrett Relation is based on MER accounting, but it has been argued that PPP accounting is more suitable.<ref name":8" /> MER accounting is used to calculate the Garrett Relation because PPP accounting is not adapted for an integrated global context focused on energy consumption where comparisons between people in various countries are not considered. Market exchange rates implicitly include estimated future value of purchases to the currency value via standard discount methods employed by traders, while PPP was designed to focus instead on present currency equivalence. Since the Garrett Relation connects past economic production to current power consumption and thus current production to future power consumption, MER accounting has been judged most appropriate.<ref name":11"/><ref name=":1" />

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